https://doi.org/10.48550/arXiv.2406.17671

Summary

  • Examine HQ Tau, intermediate mass T Tauri star undergoing magnetospheric accretion.
  • Variations in radial velocities (RV) observed in 2019-2020 cannot be solely attributed to stellar spot activity; a binary is one explanation.
  • Multi-output Gaussian process regression to model RVs and bisector inverse slopes (BIS).
  • Conclude that there is at least one companion; suspected brown dwarf.

Data

  • 39 polarimetric observations.
  • Collected over six months (2020 - 2021).
  • Four instruments:
    • SPIRou
    • ESPaDOnS
    • Neo-Narval, and
    • SOPHIE.
  • 14 observations in 2017 reported in Pouilly et al. (2020)

Data: Radial Velocities (RV)

“mean of \(V_r \approx 17\) km s−1 on a period of about 100 days”

Lomb-Scargle \(P \approx 2.5\) days.

Data: Bisector Inverse Slope (BIS)

Lomb-Scargle \(P \approx 2.42\) days.

Data

Q: Averaging bisectors throws away information?

Methodology

  1. Obtain high-res spectroscopy.
  2. Fit MOGP to RV and BIS.
    • No companion (without Keplerian modulation)
    • One companion (with Keplerian modulation)
    • Two companions (with Keplerian modulation)
  3. Compare the model fits
    • AICc
    • LOOCV

Used pyaneti package with 500 MCMC chains.

Multi-Output GP Model

  • Two response variables: RV, BIS.
  • Mean function is Keplerian function (or zero).
  • Covariance kernel: white noise (WN) + quasi-periodic (QP).
  • Interpretation of hyperaparameters:
    • \(P_{GP}\), rotation period
    • \(\lambda_e\), stellar spot lifetime
    • \(\lambda_p\), “wiggliness” within a period
    • \(T0\), transit epoch
    • \(K\), semi-amplitude

Posteriors

Results: No companion

Results: One companion

Results: One companion

  • Brown dwarf companion with minimal mass \(50.1^{+29.6}_{-32.0}\) Mjup.
  • Semi-major axis of \(\approx 0.61\) AU.
  • Period of \(126^{+32}_{-55}\) days.

Results

Conclusions

  • There is at least one companion to HQ Tau.
  • Strongly suspect a brown dwarf plus a third component.
  • Need more observations outside the inflexion point of tertiary orbital motion.

Statistical Comments

  • Fitting multiple models and comparing is a good approach, but need to be guided by physics on what’s plausible.
  • Relationship between RV and BIS is only weak/moderate.
  • Data missingness
    • Moon contamination removed 2 observations in 11/2020.
    • Dropped observations for which RV or BIS missing.
    • Three year gap between datasets.
  • “Multi-output” vs “multi-variate” vs “multi-dimensional” GP.
  • Very informative priors were used.